Operational Amplifier Applications Unit 2 – Integration and Differentiation
The top waveform in this group represents an input pulse to a passive differentiator. The
remaining waveforms show the resulting output for different relationships of input pulse width
(PW) to the RC time constant.
For the first output, RC is much smaller than the pulse width. This results in a relatively quick
charging of the capacitor and a relatively quick discharging through the resistor, as the narrow
pulse width indicates.
For the second output, RC approximately equals the pulse width. The output pulse widens as
the discharging time of the capacitor increases.
The third output shows the result of the time constant being larger than the input pulse width.
The output pulse width has increased to a point where the capacitor has not fully discharged by
the time the input pulse ends.
In practice, the most common use of a differentiator is to produce a short pulse from a relatively
long pulse.
In this active differentiator circuit, the op amp is the active element. The differentiator network
consists of a feedback resistor (RF) and an input capacitor (CIN).
At very high input frequencies, the reactance of CIN approaches zero. An input resistor (RIN) is
placed in series to limit the closed loop voltage gain at high frequencies.